My ideal game would be a bit of a blend between Starflight/Star Control II, Independence War 2, and Battlecruiser/Universal Combat (only with a much better-designed interface).
The basic gist? In another universe, formed long after this one, a strange species of chimeras (that is, they look like amalgations of other sentient races) has found some ancient starships on their planet, with no recollection of how they got there. Unfortunately, neither is in operational condition (and the databanks that store any valuable historic data are mostly corrupt), but it turns out that by taking certain components from each vessel, they can create one functional starship. Several years pass, and the project is finished. (It would have helped if they weren't stuck with 18th-century-Earth-tech upon the initial discovery.)
You play as the captain of the new starship, tasked with exploring space for myriad reasons-finding planets that can support life, discovering the history of the ships and your own race, striking good relations with any other sentient species that may exist, etc. Unfortunately, it soon becomes clear that while there are other sentients out there, they don't get along very well-some of them especially don't like YOU for reasons you'll have to discover, and will express that with their weapons. (This is basically the SF/SC2 aspect of being more about exploration, adventure, and possible diplomacy with other sentients.)
For the most part, the game plays like a space sim (and note that I do mean "sim", as in Newtonian physics, detailed subsystems and damage models, and whatnot), where you're in the pilot seat of your race's very first capital starship. Of course, you also have the option to pilot small fighters and other myriad vehicles if need be-perhaps you can pilot a boarding vessel into an enemy capital ship and fight it out within FPS-style! And, of course, you can land on planets, where it takes on a bit more of an FPRPG aspect as you wander around to build bases, find artifacts, make contact with any surface-dwelling sentients, etc.
Note that your starship has an advanced replicator that can create small ships and whatnot on the atomic level, if you have the resources. Some of those ships happen to be drones that will automatically construct a station/building out of an asteroid or planet surface (if you've played Allegiance, you'll get the basic idea). These stations could be defense posts, docks to repair and replenish your ships, colonies, etc., and thus it also has a taste of 4X as well. (Note that all the other sentient races also have these structures, which you may dock and trade with, destroy, take over, etc.)
Unfortunately, this game will never be made for obvious reasons-the scale is ludicrous. Even Derek Sm-er, 3000AD probably couldn't create a game like this, and definitely not with a decent interface!